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University of Texas at Austin ECO 339 EXTRA-CREDIT PROBLEM SET

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Question;A country produces manufactured goods, whose industry is characterized by increasing returns toscale, monopolistic competition, and firms that differentiate their products. Firms are symmetric: allfirms have identical cost functions and demand functions given below.1Q S b P PnTC F aQwhere Q is the quantity demanded when the total industry demand is S, the number of firms in theindustry is n, the average price in the industry is P and the price charged by the firm is P. TC isthe total cost of producing Q units, where F is the fixed cost of production and a is the marginalcost of production. Assume that S does not change with the price in the industry.a) Derive an equation that relates average cost AC to n, F, S, and a. That is, derive anequation with AC on the left-hand side and n, F, S and a on the other. Hint: firmsymmetry implies that each firm charges the same price. (20 pts)b) Derive an equation that relates marginal revenue MR to P, n and b. Hint: use thedemand function to get P as a function of Q.Then, multiply it by Q to get total revenue as afunction of Q. Derive marginal revenue. Then use the demand function again, to substitutefor Q. (30 pts)c) To maximize profits, firms set marginal revenue equal to ___________________. (5 pt)d) Given your answers to b) and c) derive an equation that relates P to a, b and n. (10 pts)e) Sketch the equations from a) and d) on a graph with the number of firms n on the X-axisand the average cost and price on the Y-axis. (10 pts)f) Suppose the country opens to trade, which leads to a larger market size, S. Show the effectof this on your graph from e., labeling the new price p o and the new number of firms n o.Clearly label any curves that shift, and in which direction they shift. (20 pts)

 

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